In the simplest example of scattering of two colliding particles with initial momenta p→i1,p→i2{\displaystyle {\vec {p}}_{i1},{\vec {p}}_{i2}}, resulting in final momenta p→f1,p→f2{\displaystyle {\vec {p}}_{f1},{\vec {p}}_{f2}}, the momentum transfer is given by

where the last identity expresses momentum conservation. Momentum transfer is an important quantity because Δx=ℏ/|q|{\displaystyle \Delta x=\hbar /|q|} is a better measure for the typical distance resolution of the reaction than the momenta themselves.

A wave has a momentum p=ℏk{\displaystyle p=\hbar k} and is a vectorial quantity. The difference of the momentum of the scattered wave to the incident wave is called momentum transfer. The wave number k is the absolute of the wave vectork=q/ℏ{\displaystyle k=q/\hbar } and is related to the wavelengthk=2π/λ{\displaystyle k=2\pi /\lambda }. Often, momentum transfer is given in wavenumber units in reciprocal lengthQ=kf−ki{\displaystyle Q=k_{f}-k_{i}}

The presentation in Q{\displaystyle Q}-space is generic and does not depend on the type of radiation and wavelength used but only on the sample system, which allows to compare results obtained from many different methods. Some established communities such as powder diffraction employ the diffraction angle 2θ{\displaystyle 2\theta } as the independent variable, which worked fine in the early years when only a few characteristic wavelengths such as Cu-Kα{\displaystyle \alpha } were available. The relationship to Q{\displaystyle Q}-space is